Convergence rates for the reaction coefficient and the initial temperature identification problems

In this paper, we investigate the convergence rates of the inverse heat transfer problem of simultaneously determining the space-dependent reaction coefficient and the initial temperature from some additional temperature observations. The strategy is to decouple the original problem into two inverse problems: (i) recover the reaction coefficient; (ii) determine the initial temperature with the estimated reaction coefficient in the previous stage. The Tikhonov regularization method is used to reconstruct the reaction coefficient, and a new source condition is used to derive the convergence rates to the reaction coefficient. Based on the approximated reaction coefficient, the initial temperature as well as its convergence rates can be obtained by using the quasi-reversibility method.